Geometric Algebra: Signs of electromagnetic field tensor components?

Here's a question that may look like an E&M question, but is really just a geometric algebra question. In particular, I've got a sign off by 1 somewhere I think and I wonder if somebody can spot it.

PF isn't accepting what I wrote (my latex appears to trigger an internal database error), so I've converted it to standalone latex and attached my notes and question as a pdf file. I've also attached what I attempted to post to PF, for reply purposes (so it can be cut and pasted from selectively if desired).

I don't see a mistake in my calculation, but the sign is inverted compared to the text (also in the pdf file). Since this isn't listed in the errata even after two editions my assumption was that I had am error in my calculation somewhere.

I don't see a mistake in my calculation, but the sign is inverted compared to the text (also in the pdf file). Since this isn't listed in the errata even after two editions my assumption was that I had am error in my calculation somewhere.

Actually, I second guess myself about the factor of two. For the sum only one of the pairs of deltas can be non-zero, so you only need the factor of two if one were to define

[tex]
F = \sum F^{\mu\nu} \gamma_{\mu} \wedge \gamma_{\nu}
[/tex]

(summing over all indexes instead). Again, a few more details in the book would have been good, unless the intention was for the reader to understand all this a lot better by figuring it out themselves:)

Note that this is opposite from what I used in all the subsequent calculations, which explains the off by one sign for just the B parts.

So, ... I think I now understand all the notation implied in those few pages, as well as see that there is no typo there (which makes sense given that this is a few times reprinted and its not in the errata).

Actually, what you said was very helpful. Only when I tried to reply to your post did I realize exactly what was meant by [itex]F^{\mu\nu}[/itex]. It really isn't defined without one of the sums above (which isn't in the text). Once you pick one of those as the definition it explains the ordering choice of the reciprocal frame bivector basis to take dot products with.